Let (X-i)(i >= 1) be a sequence of positive independent identically distributed random variables with regularly varying distribution tail of index 0 < alpha < 1 and define
T-n:= X-1(2) + X-2(2) + ... + X-n(2) / (X-1 + X-2 + ... + X-n)(2).
In this note we simplify an expression for (n ->infinity) lim E(T-n(k)), which was obtained by ALBRECHER and TEUGELS: A symptotic analysis of a measure of variation. Theory Prob. Math. Stat., 74(2006), 1-9, in terms of coefficients of a continued fraction expansion. The new formula establishes an unexpected link to an enumeration problem for rooted maps on orientable surfaces that was studied in ARQUES and BERAUD: Rooted maps of orientable surfaces, Riccati's equation and continued fractions. Discrete Mathematics, 215 (2000), 1-12.